1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_TRANSLATION_H
11#define EIGEN_TRANSLATION_H
12
13namespace Eigen {
14
15/** \geometry_module \ingroup Geometry_Module
16 *
17 * \class Translation
18 *
19 * \brief Represents a translation transformation
20 *
21 * \tparam _Scalar the scalar type, i.e., the type of the coefficients.
22 * \tparam _Dim the dimension of the space, can be a compile time value or Dynamic
23 *
24 * \note This class is not aimed to be used to store a translation transformation,
25 * but rather to make easier the constructions and updates of Transform objects.
26 *
27 * \sa class Scaling, class Transform
28 */
29template<typename _Scalar, int _Dim>
30class Translation
31{
32public:
33 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
34 /** dimension of the space */
35 enum { Dim = _Dim };
36 /** the scalar type of the coefficients */
37 typedef _Scalar Scalar;
38 /** corresponding vector type */
39 typedef Matrix<Scalar,Dim,1> VectorType;
40 /** corresponding linear transformation matrix type */
41 typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
42 /** corresponding affine transformation type */
43 typedef Transform<Scalar,Dim,Affine> AffineTransformType;
44 /** corresponding isometric transformation type */
45 typedef Transform<Scalar,Dim,Isometry> IsometryTransformType;
46
47protected:
48
49 VectorType m_coeffs;
50
51public:
52
53 /** Default constructor without initialization. */
54 EIGEN_DEVICE_FUNC Translation() {}
55 /** */
56 EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy)
57 {
58 eigen_assert(Dim==2);
59 m_coeffs.x() = sx;
60 m_coeffs.y() = sy;
61 }
62 /** */
63 EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
64 {
65 eigen_assert(Dim==3);
66 m_coeffs.x() = sx;
67 m_coeffs.y() = sy;
68 m_coeffs.z() = sz;
69 }
70 /** Constructs and initialize the translation transformation from a vector of translation coefficients */
71 EIGEN_DEVICE_FUNC explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
72
73 /** \brief Retruns the x-translation by value. **/
74 EIGEN_DEVICE_FUNC inline Scalar x() const { return m_coeffs.x(); }
75 /** \brief Retruns the y-translation by value. **/
76 EIGEN_DEVICE_FUNC inline Scalar y() const { return m_coeffs.y(); }
77 /** \brief Retruns the z-translation by value. **/
78 EIGEN_DEVICE_FUNC inline Scalar z() const { return m_coeffs.z(); }
79
80 /** \brief Retruns the x-translation as a reference. **/
81 EIGEN_DEVICE_FUNC inline Scalar& x() { return m_coeffs.x(); }
82 /** \brief Retruns the y-translation as a reference. **/
83 EIGEN_DEVICE_FUNC inline Scalar& y() { return m_coeffs.y(); }
84 /** \brief Retruns the z-translation as a reference. **/
85 EIGEN_DEVICE_FUNC inline Scalar& z() { return m_coeffs.z(); }
86
87 EIGEN_DEVICE_FUNC const VectorType& vector() const { return m_coeffs; }
88 EIGEN_DEVICE_FUNC VectorType& vector() { return m_coeffs; }
89
90 EIGEN_DEVICE_FUNC const VectorType& translation() const { return m_coeffs; }
91 EIGEN_DEVICE_FUNC VectorType& translation() { return m_coeffs; }
92
93 /** Concatenates two translation */
94 EIGEN_DEVICE_FUNC inline Translation operator* (const Translation& other) const
95 { return Translation(m_coeffs + other.m_coeffs); }
96
97 /** Concatenates a translation and a uniform scaling */
98 EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
99
100 /** Concatenates a translation and a linear transformation */
101 template<typename OtherDerived>
102 EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;
103
104 /** Concatenates a translation and a rotation */
105 template<typename Derived>
106 EIGEN_DEVICE_FUNC inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const
107 { return *this * IsometryTransformType(r); }
108
109 /** \returns the concatenation of a linear transformation \a l with the translation \a t */
110 // its a nightmare to define a templated friend function outside its declaration
111 template<typename OtherDerived> friend
112 EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)
113 {
114 AffineTransformType res;
115 res.matrix().setZero();
116 res.linear() = linear.derived();
117 res.translation() = linear.derived() * t.m_coeffs;
118 res.matrix().row(Dim).setZero();
119 res(Dim,Dim) = Scalar(1);
120 return res;
121 }
122
123 /** Concatenates a translation and a transformation */
124 template<int Mode, int Options>
125 EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const
126 {
127 Transform<Scalar,Dim,Mode> res = t;
128 res.pretranslate(m_coeffs);
129 return res;
130 }
131
132 /** Applies translation to vector */
133 template<typename Derived>
134 inline typename internal::enable_if<Derived::IsVectorAtCompileTime,VectorType>::type
135 operator* (const MatrixBase<Derived>& vec) const
136 { return m_coeffs + vec.derived(); }
137
138 /** \returns the inverse translation (opposite) */
139 Translation inverse() const { return Translation(-m_coeffs); }
140
141 Translation& operator=(const Translation& other)
142 {
143 m_coeffs = other.m_coeffs;
144 return *this;
145 }
146
147 static const Translation Identity() { return Translation(VectorType::Zero()); }
148
149 /** \returns \c *this with scalar type casted to \a NewScalarType
150 *
151 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
152 * then this function smartly returns a const reference to \c *this.
153 */
154 template<typename NewScalarType>
155 EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
156 { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
157
158 /** Copy constructor with scalar type conversion */
159 template<typename OtherScalarType>
160 EIGEN_DEVICE_FUNC inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
161 { m_coeffs = other.vector().template cast<Scalar>(); }
162
163 /** \returns \c true if \c *this is approximately equal to \a other, within the precision
164 * determined by \a prec.
165 *
166 * \sa MatrixBase::isApprox() */
167 EIGEN_DEVICE_FUNC bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
168 { return m_coeffs.isApprox(other.m_coeffs, prec); }
169
170};
171
172/** \addtogroup Geometry_Module */
173//@{
174typedef Translation<float, 2> Translation2f;
175typedef Translation<double,2> Translation2d;
176typedef Translation<float, 3> Translation3f;
177typedef Translation<double,3> Translation3d;
178//@}
179
180template<typename Scalar, int Dim>
181EIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType
182Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
183{
184 AffineTransformType res;
185 res.matrix().setZero();
186 res.linear().diagonal().fill(other.factor());
187 res.translation() = m_coeffs;
188 res(Dim,Dim) = Scalar(1);
189 return res;
190}
191
192template<typename Scalar, int Dim>
193template<typename OtherDerived>
194EIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType
195Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const
196{
197 AffineTransformType res;
198 res.matrix().setZero();
199 res.linear() = linear.derived();
200 res.translation() = m_coeffs;
201 res.matrix().row(Dim).setZero();
202 res(Dim,Dim) = Scalar(1);
203 return res;
204}
205
206} // end namespace Eigen
207
208#endif // EIGEN_TRANSLATION_H
209